Problem: What's the first wrong statement in the proof below that $ \triangle CEB \cong \triangle CAB$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{BC} \cong \overline{BD}$ $, \ $ $ \angle ABC \cong \angle DBE$ $, \ $ $ \angle BAC \cong \angle BED$ $, \ $ $ \angle ABC \cong \angle CFE$ $, \ $ $ \overline{AB} \cong \overline{EF}$ $, \ $ and $\ $ $ \angle BAC \cong \angle CEF$ Proof $ \triangle DEB \cong \triangle CAB$ because AAS $ \overline{BE} \cong \overline{AB}$ because corresponding parts of congruent triangles are congruent $ \triangle CEF \cong \triangle DEB$ because ASA $ \angle CBE \cong \angle BED$ because alternate interior angles are equal $ \triangle CAB \cong \triangle CEF$ because ASA $ \triangle CEB \cong \triangle CAB$ because SSS
Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \triangle DEB \cong \triangle CEF$ is the first wrong statement.